Troelstra's Paradox and Markov's Principle

Mark van Atten (1)

1 SND - Sciences, Normes, Décision

A prominent problem for the Theory of the Creating Subject is Troelstra's Paradox. As is well known, the construction of that paradox depends on the acceptability of a certain impredicativity, of a kind that some intuitionists accept and others do not. After a presentation of the Theory of the Creating Subject and the paradox, I argue that the paradox moreover depends on Markov's Principle, in a form that no intuitionist should accept. A postscript discusses a new version of the paradox that Troelstra has proposed in reaction to my argument.

Mots clés: Intuitionism; L.E.J. Brouwer; Markov's Principle; A. Troelstra

Domaines: Philosophie; Mathématiques [math]

Mark van Atten. Troelstra's Paradox and Markov's Principle. 2016. ⟨hal-01415603⟩